In a small bowl, whisk together the flour and salt. Set aside.
In a large mixing bowl, beat the softened butter with an electric mixer until smooth and creamy.
Add the powdered sugar, lemon zest, and lemon juice. Beat until light and fluffy.
Gradually add the flour mixture and mix on low speed until a crumbly dough forms.
Turn the dough onto a sheet of parchment paper and press it together into a disc.
Place another sheet of parchment paper on top and roll the dough to approximately 1/4-inch thickness.
Transfer the dough to the refrigerator and chill for 1 hour or until firm.
Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.
Remove the chilled dough and cut cookies using a 3-inch scalloped cookie cutter.
Arrange cookies on the prepared baking sheet, leaving about 1 inch between each.
Re-roll scraps as needed. If the dough becomes soft, chill again for 15 minutes before baking.
Bake for 14–15 minutes, or until the edges begin to turn lightly golden.
Cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.
For the icing, stir together powdered sugar and lemon juice until smooth and drizzleable.
Transfer icing to a piping bag and drizzle over cooled cookies.
Sprinkle fresh lemon zest over the icing before it sets.
Allow the icing to harden before serving.